WAEC 2023 · Paper 1 · Q35

Statics: forces, equilibrium & moments

A uniform beam $PQ$ of length 80 cm and weight 60 N rests on a support at $X$ where $|PX| = 30$ cm. If the body is kept in equilibrium by a mass $m$ kg which is placed at $P$ , calculate the value of $m$ . [Take $g = 10\ \text{m s}^{-2}$ ]

Worked solution (try it first)

The beam is uniform, so its 60 N weight acts at the middle, 40 cm from $P$ , which is $40 - 30 = 10$ cm from $X$ .
The mass at $P$ has weight $10m$ N, acting 30 cm from $X$ on the other side.
Take moments about $X$ : $10m \times 30 = 60 \times 10$ , so $300m = 600$ .
So $m = 2.0$ , option A.

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